Bevelling concave curve part results in buggy mesh
What you are seeing are shading artifacts from intersecting geometry.

Very tight sharp corners always cause problems when beveling in graphics software in general, since the software can't automatically handle these hard corner-cases cases unless it is specifically programmed to, or an option exists to clip/trim or extend said bevel options.

Blender has no special tools to deal with these so they end up self intersecting.

I usually solve it with the Offset modification available to the left of Bevel value.

Since beveling offsets the curve "outside" by the same amount of units used as bevel factor, all you have to do is counter this by using that value as a negative factor for offset so Blender "insets" the growth.



Additionally you may want to add an Edge Split modifier to your curve to avoid smoothing artifacts or errors.